Elementary School Students\u27 Quantitative Reasoning: Processing Whole Numbers and Proportions

Elementary school-aged children have great difficulty reasoning proportionally and struggle with fractions and decimals, theoretically because proportions do not abide by the same principles as more familiar whole number quantities. The present study examines individual differences in proportional reasoning and whole number representations and tests a prediction for a nonlinearity in the development of relations between the two. Pre-kindergarten through fifth-grade students completed a battery of computerized tasks, including a proportional reasoning task, “which is more?” and “which is #?” whole number comparison tasks, and symbolic and nonsymbolic numerical line-estimation tasks. The results indicate that though younger children’s performance on each of the whole number comparison and number line estimation tasks were significantly positively correlated, performance on each was negatively correlated with performance on the proportional reasoning task. By contrast, older children’s performance on the proportional, whole number comparison, and number line estimation tasks were all positively correlated. These findings support the proposal that better counting abilities early in development interfere with early proportional reasoning capacities, though the two are positively related later in development

The Sensititivity of Five- to Ten-Year-Old Children to Value, Probability, and Loss

Classic and contemporary researchers have studied the child's abilities to discriminate quantitative values, understand probability, and appreciate risk and uncertainty. The current studies were designed to extend and methodologically integrate recent insights that have been made across these sub-areas. A computerized decision-making task, which allows manipulation of probability of success and quantitative outcome value, was developed. In the first study, this task was used to analyze the development of preference between options with systematically contrasted numerical outcome values. Contrary to recent research, this study revealed that participants, and particularly younger children (i.e., five- and six-year-olds), tend to neglect quantitative outcome value information, and seem to base choices primarily on probability information. In the second study, the task was used to assess the development of preference between options with systematically contrasted probabilities of success. Consistent with recent research, this study revealed that even young participants attend to differences in probability of success between decision alternatives; however, younger participants seemed less able to explicitly integrate decision outcomes, as assessed by more explicit measures of probability understanding. In the third study, probability of success was again manipulated, but wins were combined with losses. This study revealed, like Study 2, that children adjusted preference as a function of probability of success; however, consistent with Study 1, this study revealed that children tend to neglect outcome values. Cross-study analyses were conducted which further demonstrated that decision-making probabilities loom larger than outcome values. Collectively, these studies suggest that processing of probabilities developmentally precedes processing of quantitative outcome values, and that implicit processing developmentally precedes explicit decision integration. In the conclusion these findings and possible future directions are discussed

Spatial Attention to Social Cues is not a Monolithic Process

Social stimuli are a highly salient source of information, and seem to possess unique qualities that set them apart from other well-known categories. One characteristic is their ability to elicit spatial orienting, whereby directional stimuli like eyegaze and pointing gestures act as exogenous cues that trigger automatic shifts of attention that are difficult to inhibit. This effect has been extended to non-social stimuli, like arrows, leading to some uncertainty regarding whether spatial orienting is specialized for social cues. Using a standard spatial cueing paradigm, we found evidence that both a pointing hand and arrow are effective cues, but that the hand is encoded more quickly, leading to overall faster responses. We then extended the paradigm to include multiple cues in order to evaluate congruent vs. incongruent cues. Our results indicate that faster encoding of the social cue leads to downstream effects on the allocation of attention resulting in faster orientin

Asymmetrical Interference Effects Between Two-Dimensional Geometric Shapes and Their Corresponding Shape Words

Nativists have postulated fundamental geometric knowledge that predates linguistic and symbolic thought. Central to these claims is the proposal for an isolated cognitive system dedicated to processing geometric information. Testing such hypotheses presents challenges due to difficulties in eliminating the combination of geometric and non-geometric information through language. We present evidence using a modified matching interference paradigm that an incongruent shape word interferes with identifying a two-dimensional geometric shape, but an incongruent two-dimensional geometric shape does not interfere with identifying a shape word. This asymmetry in interference effects between two-dimensional geometric shapes and their corresponding shape words suggests that shape words activate spatial representations of shapes but shapes do not activate linguistic representations of shape words. These results appear consistent with hypotheses concerning a cognitive system dedicated to processing geometric information isolated from linguistic processing and provide evidence consistent with hypotheses concerning knowledge of geometric properties of space that predates linguistic and symbolic thought

Probabilistic Cue Combination: Less is More

Learning about the structure of the world requires learning probabilistic relationships: rules in which cues do not predict outcomes with certainty. However, in some cases, the ability to track probabilistic relationships is a handicap, leading adults to perform non-normatively in prediction tasks. For example, in the dilution effect, predictions made from the combination of two cues of different strengths are less accurate than those made from the stronger cue alone. Here we show that dilution is an adult problem; 11-month-old infants combine strong and weak predictors normatively. These results extend and add support for the less is more hypothesis: limited cognitive resources can lead children to represent probabilistic information differently from adults, and this difference in representation can have important downstream consequences for prediction

Stroop Interference in a Delayed Match-To-Sample Task: Evidence for Semantic Competition

Discussions of the source of the Stroop interference effect continue to pervade the literature. Semantic competition posits that interference results from competing semantic activation of word and color dimensions of the stimulus prior to response selection. Response competition posits that interference results from competing responses for articulating the word dimension vs. the color dimension at the time of response selection. We embedded Stroop stimuli into a delayed match-to-sample (DMTS) task in an attempt to test semantic and response competition accounts of the interference effect. Participants viewed a sample color word in black or colored fonts that were ongruent or incongruent with respect to the color word itself. After a 5 s delay, participants were presented with two targets (i.e., a match and a foil) and were instructed to select the correct match. We probed each dimension independently during target presentations via color targets (i.e., two colors) or word targets (i.e., two words) and manipulated whether the semantic content of the foil was related to the semantic content of the irrelevant sample dimension (e.g., word sample “red” in blue font with the word “red” as the match and the word “blue” as the foil). We provide evidence for Stroop interference such that response times (RTs) increased for incongruent trials even in the presence of a response option with semantic content unrelated to the semantic content of the irrelevant sample dimension. Accuracy also deteriorated during the related foil trials. A follow-up experiment with a 10 s delay between sample and targets replicated the results. Results appear to provide converging evidence for Stroop interference in a DMTS task in a manner that is consistent with an explanation based upon semantic competition and inconsistent with an explanation based upon response competition

Do Eye Movements During Shape Discrimination Reveal an Underlying Geometric Structure?

Using a psychophysical approach coupled with eye-tracking measures, we varied length and width of shape stimuli to determine the objective parameters that corresponded to subjective determination of square/rectangle judgments. Participants viewed a two-dimensional shape stimulus and made a two-alternative forced-choice whether it was a square or rectangle. Participants’ gaze was tracked throughout the task to explore directed visual attention to the vertical and horizontal axes of space. Behavioral results provide threshold values for two-dimensional square/rectangle perception, and eye-tracking data indicated that participants directed attention to the major and minor principal axes. Results are consistent with the use of the major and minor principal axis of space for shape perception and may have theoretical and empirical implications for orientation via geometric cues

Is automatic imitation a specialized form of stimulus–response compatibility? Dissociating imitative and spatial compatibilities

In recent years research on automatic imitation has received considerable attention because it represents an experimental platform for investigating a number of inter-related theories suggesting that the perception of action automatically activates corresponding motor programs. A key debate within this research centers on whether automatic imitation is any different than other long-term S-R associations, such as spatial stimulus-response compatibility. One approach to resolving this issue is to examine whether automatic imitation shows similar response characteristics as other classes of stimulus-response compatibility. This hypothesis was tested by comparing imitative and spatial compatibility effects with a two alternative forced-choice stimulus-response compatibility paradigm and two tasks: one that involved selecting a response to the stimulus (S-R) and one that involved selecting a response to the opposite stimulus (OS-R), i.e., the one not presented. The stimulus for both tasks was a left or right hand with either the index or middle finger tapping down. Speeded responses were performed with the index or middle finger of the right hand in response to the finger identity or the left-right spatial position of the fingers. Based on previous research and a connectionist model, we predicted standard compatibility effects for both spatial and imitative compatibility in the S-R task, and a reverse compatibility effect for spatial compatibility but not for imitative compatibility in the OS-R task. The results from the mean response times, mean percentage of errors, and response time distributions all converged to support these predictions. A second noteworthy result was that the recoding of the finger identity in the OS-R task required significantly more time than the recoding of the left-right spatial position, but the encoding time for the two stimuli in the S-R task was equivalent. In sum, this evidence suggests that the processing of spatial and imitative compatibility is dissociable with regard to two different processes in dual processing models of stimulus-response compatibility

Mapping Dynamic Histone Acetylation Patterns to Gene Expression in Nanog-depleted Murine Embryonic Stem Cells

Embryonic stem cells (ESC) have the potential to self-renew indefinitely and to differentiate into any of the three germ layers. The molecular mechanisms for self-renewal, maintenance of pluripotency and lineage specification are poorly understood, but recent results point to a key role for epigenetic mechanisms. In this study, we focus on quantifying the impact of histone 3 acetylation (H3K9,14ac) on gene expression in murine embryonic stem cells. We analyze genome-wide histone acetylation patterns and gene expression profiles measured over the first five days of cell differentiation triggered by silencing Nanog, a key transcription factor in ESC regulation. We explore the temporal and spatial dynamics of histone acetylation data and its correlation with gene expression using supervised and unsupervised statistical models. On a genome-wide scale, changes in acetylation are significantly correlated to changes in mRNA expression and, surprisingly, this coherence increases over time. We quantify the predictive power of histone acetylation for gene expression changes in a balanced cross-validation procedure. In an in-depth study we focus on genes central to the regulatory network of Mouse ESC, including those identified in a recent genome-wide RNAi screen and in the PluriNet, a computationally derived stem cell signature. We find that compared to the rest of the genome, ESC-specific genes show significantly more acetylation signal and a much stronger decrease in acetylation over time, which is often not reflected in an concordant expression change. These results shed light on the complexity of the relationship between histone acetylation and gene expression and are a step forward to dissect the multilayer regulatory mechanisms that determine stem cell fate.Comment: accepted at PLoS Computational Biolog

Author Correction: A consensus-based transparency checklist.

An amendment to this paper has been published and can be accessed via a link at the top of the paper